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full N-ary tree has M non-leaf nodes, how many leaf nodes does it have? Discuss it! Use Geometric progression. M + (N ^ (n-1)) = (1 - (N ^ n)) / (1 - N) Here (N ^ (n-1)) is the number of leaf-nodes. Solving for this leads to the answer Leaf nodes = M * (N - 1) + 1 Suppose you have a 3-ary tree A B C D E F G H I J K L M So, here M=4 and N=3. So using the formula above, Leaf nodes = M * (N - 1) + 1 = 4 * (3 - 1) + 1 = 9